Integration practice questions

Secondary 4 topics from the Additional Mathematics 4049 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

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What this topic covers

Worked examples

Example 1

Find ∫(x+5)4 dx\int (x + 5)^{4} \, dx.
Show the worked solution
  • $\int (x + 5)^{4} \, dx = \frac{(x + 5)^{5}}{5 \times 1} + c \quad \scriptsize\textit{linear chain rule}$
  • $= \frac{1}{5}(x + 5)^{5} + c$

Answer: 1/5(x+5)5+c1/5(x+5)^5+c

Example 2

Find ∫30sec⁡2(6x) dx\int 30\sec^2(6x) \, dx.
Show the worked solution
  • $\int 30\sec^2(6x) \, dx = 30 \cdot \frac{1}{6}\tan(6x) + c \quad \scriptsize\textit{reverse of } \frac{d}{dx}[\tan(6x)]$
  • $= 5\tan(6x) + c$

Answer: 5tan(6x)+c5tan(6x)+c

Example 3

Find ∫8e4x+4 dx\int 8e^{4x + 4} \, dx.
Show the worked solution
  • $\int 8e^{4x + 4} \, dx = \frac{8}{4} e^{4x + 4} + c \quad \scriptsize\textit{linear exponent rule}$
  • $= 2e^{4x + 4} + c$

Answer: 2e4x+4+c2e^{4x+4}+c

Questions parents ask

Is it really free?

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Which syllabus does this follow?

Additional Mathematics (4049), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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